Constitutive Law And Stability Of Electroactive Dielectric Elastomers

For a long time, researchers have been working on the study of hard materials widely applied in the field of engineering. In the natural world, however, the main structures of animals and plants are usually composed of soft materials. Compared with traditional hard materials which are exemplified by metals and ceramics, electroactive dielectric elastomer (DE) is a typical category of soft materials. It was first developed by Stanford Research Institute International (SRI) in the1990s. When subjected to electric fields, DEs can exhibit large deformation and are characterized by their merits of high elastic energy density, short response time, high efficiency, light mass, etc. DEs are primarily used as actuators, artificial arms, facial expressions, bionic robots, airship rudders, energy harvesters and Braille display equipments, which have shown great potential applications in the fields of artificial muscle, intelligent bionics, aerospace, mechanical engineering and so on.In this thesis, the mechanical and stability behaviors of dielectric elastomers as soft materials have been studied. Wihtin the classical thermodynamics theoretical framework, by considering different types of free energy functions of dielectric elastomers subjected to mechanical-electrical (or mechanical-electrical-thermal) coupling physical fields, the constitutive equations of this special material have been deduced, and accordingly the electromechanical stability and snap-through stability of dielectric elastomers have been analyzed thoroughly. The typical failure modes of the dielectric elastomers experienced include loss of tension, rupture, loss of charge, electrical breakdown, and electromechanical instability. On this basis the author has traced out the allowable areas of dielectric elastomers and accordingly determined the energy density of energy harvester using DEs in this thesis. A stack energy harvester has been designed and manufactured and its overall properties have been examined experimently. The changes of temperatures and entropies of dielectric elastomers and electrocaloric materials caused by voltages imposed on them have also been obtained. According these results, it has proved that high polar liquid dielectrics may possess a large electrocaloric effect. In the meantime, a typical thermodynamic cycle has been depicted in order to predicted the refrigerating capacity of electrocaloric materials based cooling devices.Firstly, the constitutive relation and electromechanical stability of ideal dielectric elastomers undergoing large deformation have been investigated. Based on the thermodynamics theory, the constitutive equations have been constructed in which Mooney-Rivlin elastic strain energy function has been used. The critical nominal electric fields have been yielded for different dielectric materials or structures in terms of the material constant ratio,. The results show that the larger material constant ratio is, the more stable dielectric elastomer or structure tend to be. This conclusion is then extended to the electromechanical stability analysis of ideal elastomers based on elastic strain energy functions with multiple material constants. Furthermore, the allowable areas of Mooney-Rivlin type ideal dielectric elastomers under either equal biaxial stretch or unequal biaxial stretch have been determined. In addition, the energy generated by ideal dielectric elastomer energy harvester in one cycle has beeen calculated. A buoy-like generator contains three DE stacks has been designed and manufactured to demonstrate the effectiveness of DE used in energy harvesters which aims to glean wave energy and preliminary tests about its properties have been carried out.Secondly, based on the experimental data of dielectric elastomer’s permittivity, an expression of permittivity varying nonlinearly with stretch has been proposed. The electromechanical stability of DE has been discussed based on both numerical analyses and analytical expressions. The analytical expressions of electromechanical stability parameters, such as nominal and true stresses, critical nominal and true electric fields, critical stretch and so on, have been obtained. The simplified expressions of these analytical parameters for DE subjected to equal biaxial stretch have also been deduced. Very good agreement exists between the numerical results, analytical results and experimental data.Thridly, in this thesis, the constitutive theory and electromechanical stability of dielectric elastomer composite materials have also been investigated. According to the experimental data, by the method of constructing apparent elastic modulus expressions in the composite material theory, two kinds of permittivity expressions of dielectric elastomer composite materials have been proposed based on particle content and electrostriction deformation respectively. Accordingly, the electric field energy in the systems has been established further. The free energy function of the thermodynamic systems has been constructed based on Knowles elastic strain energy function which couples multiple material constants. Besides, the constitutive function in the equilibrium state has been conducted. Based on these, the electromechanical stability of dielectric elastomer composite material thermodynamic systems has been analyzed, and the influences of particle content and electrostriction on the stability have been discussed. Experiments have been carried out to investigate the electrically induced deformation of silicon rubber based dielectric elastomer composite materials and to validate the numerical results. Moreover, the thermodynamic properties of thermo-dielectric elastomers and electrocaloric materials have been analyzed. An expression of permittivity depending on temperature and stretch has been proposed. The expression of thermal contribution has been conducted based on the relationship among free energy, internal energy and entropy.Fourthly, the influence of temperature on dielectric elastomer thermo-electro-mechanical coupling systems has been described in terms of thermal contribution. The free energy function has been built for dielectric elastomer thermodynamic system in adiabatic circumstances, and the corresponding constitutive function has been deduced. In addition, the thermodynamic properties of dielectric elastomers undergoing variable temperatures and electric fields have been studied. At the same time, the thermo-electro-mechanical stability of dielectric elastomers under either equal biaxial or unequal biaxial stretch has been discussed. Furthermore, the allowable areas of dielectric elastomers in either equal or unequal biaxial circumstances, as well as temperature changes and entropy changes of dielectric elastomers and electrocaloric materials induced by variations of electrical fields, have been discussed and calculated. The similar Carnot thermodynamic cycles have bben described for electrocaloric materials as refrigerators and the refrigerating capacity parameters have been evaluated. These numerical results can be used to guide the design and manufacture of devices based on dielectric elastomers and electrocaloric materials with variable ambient temperature.Finally, the constitutive relation and stability of dielectric elastomers undergoing polarization saturation has been discussed. Subject to a voltage, the charge will be induced on the compliant electrodes of a dielectric elastomer. When the voltage is small, the charge increases with the voltage. Along with the continuously increase of voltage, when the charge approaches a certain value, it won’t increase any more and become saturated. This process is called the polarization saturation of dielectric elastomers. A thermodynamic model of dielectric elastomers has been proposed, which couples nonlinear dielectric behavior with hyperelastic behavior. Maxwell stresses have been acquired in the circumstances of linear and nonlinear dielectric behaviors respectively. It has been predicted that dielectric elastomers undergoing polarization saturation can exhibit giant deformation. Meanwhile, the electromechanical stability and snap-through stability have also been investigated while dielectric elastomers undergoing polarization saturation. Furthermore, the influence of strain hardening on the electromechanical deformation exhibited by dielectric elastomers has been analyzed. It is proved that the electromechanical stability and snap-through stability can dramatically influenced by the polymers’ stretch limits and dipoles’polarization saturation. Based on these results, it is suggested that dielectric elastomers can exhibit giant electromechanical deformation as long as they undergo snap-through stability and avoid electrical breakdown and electromechanical instability.